Home > Triangles > Triangle – Area problem

Triangle – Area problem

In triangle ABC, cevians AD, BE and CF intersect at point P. The areas of triangles PAF, PFB, PBD and PCE are 40, 30, 35 and 84, respectively. Find the area of triangle ABC.

TIPS:Let the area of triangle PEA be x and area of triangle PCD be y . Now use the proportion of areas of triangles.

\frac{y}{35} = \frac{ 84+ x +y }{105} \: and \: \frac{84}{x} = \frac{ 119+y }{ 70 + x }

Now use system of linear equations and find x and y . The area of triangle ABC is 189+x+y .

 

Advertisements
  1. No comments yet.
  1. No trackbacks yet.

Leave a Reply

Please log in using one of these methods to post your comment:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s

%d bloggers like this: